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Bertrand theorem permits closed orbits in 3d Euclidean space only for 2 typesof central potentials. These are of Kepler-Coulomb and harmonic oscillatortype. Volker Perlick recently extended Bertrand theorem. He designed new staticspherically symmetric (Bertrand) spacetimes obeying Einsteins equations andsupporting closed orbits. In this work we prove that the topology and geometryof these spacetimes permits to solve quantum many-body problem for any atom ofperiodic system exactly. The computations of spectrum for any atom of periodicsystem becomes analogous to that for hydrogen atom. Initially the exactsolution of the Schr\"odinger equation for any multielectron atom was obtainedby Tietz in 1956. However, neither himself nor others fully comprehended whatactually was obtained. We recalculated Tietz results by applying themethodology consistent with new (different from that developed by Fock in 1936)way of solving Schro"odingers equation for hydrogen atom. In the light of thisnew result it had become possible to demonstrate rigorously that the Tietz-typeSchro"odingers equation is in fact describing the quantum motion in Bertrandspacetime. As a bonus, we obtained the analytical proof of the Madelung ruledefined in the text

How the modified Bertrand theorem explains regularities of the periodic table I. From conformal invariance to Hopf mapping